Is there a way to use grid fill with the mirror modifier?
It is possible only with some preparation.

GridFill uses closed loop to work on and adjacent number of vertices. You can't use it if you have opened loop (ready to be mirrored). The Mirror modifier won't change anything as the geometry it creates doesn't exist unless the modifier is applied. So you are left with 2 general ways:


Applying modifier temporarily


Apply modifier, make necessary changes.
Remove half of the mesh. It is ready to be mirrored again.
Add modifier back.

Create geometry necessary for GridFill manually.


Select 2 vertices which are located on the mirror plane (those connected only to one edge).
Create an edge (with F).
Subdivide it. The number of subdivisions depends on number of the vertices of the rest of the mesh. In case of circle from 32 vertices, subdivide 7 times (so to create 7 additional vertices).
Select all and use Ctrl+F > GridFill (probably modifiy its settings a bit).



The half of the mesh will be filled with the quad topology reflected in the mirrored part.